How does a foreigner go about getting a Visa credit card in China?

I would say extremely difficult to get one. You must have a steady job and good income for over one year, have work permit and residence permit, and of course, anj account with the bank and some sort of credit record.
I gave up on getting one, I do use the debit card from a savings account instead.
I even tried to get a prepaid one, and Bank of China refused it. But I do have heard that Construction Bank is issuing credit cards to foreigners, a couple of my friends managed to get one, but their credit limit is 600 Rmb. For that to me is not worth the effort.
Bank of China told me that they are reluctant because they feel foreigners will run up the tab, and then go home and "forget" the payments. Maybe they are not too far off in their thinking, since most foreigners in China are here temporarely.